I have spent hours on this, and I believe I need a match, offset, index, but not sure which order.

I am trying to total cells until they are greater than the value in another cell and then pull in the date from an adjacent cell when they are.

I have dates in E2 to R2
I have numbers in E3 to R3

I have a value in B3

I want to total E3 to R3 until the sum is greater then the value in B3, when it reaches that point, I want to pull the corresponding date from cells E2 to R2.
The result needs to be in cell A3